Primal‐dual interior‐point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

In this paper we propose primal‐dual interior‐point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are $O(\sqrt{n}\log (\frac{n}{\epsilon }))$ for small‐update methods and $O(n^{\frac{3}{4}}\log (\frac{n}{\epsilon }))$ for large‐update, respectively. The resulting bound is better than the classical kernel function. For small‐update, the iteration complexity is the best known bound for such methods.